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The USS Lyon was a US Navy ship involved in WWII. All ships involved in WWII are currently decommissioned or in a museum.

USNavyShip(theUSSLyon) ∧ InvolvedIn(theUSSLyon, wWII) ∀x (InvolvedIn(x, wWII) → (CurrentlyDecommissioned(x) ∨ In(x, museum)))

The USS Lyon is currently decommissioned.

CurrentlyDecommissioned(theUSSLyon)

Uncertain

All disposables are designed to be used only once. Some items used in Tom's house are eco-friendly. Every item used in Tom's house is either disposable or reusable. If something is made from metal, then it is not made from plastic. All reusable items used in Tom's house are made from metal. The chopsticks used in Tom's house are either made from metals and plastics, or that they are neither made from metals nor plastics.

∀x (Disposable(x) → DesignedToBeOnlyUsedOnce(x)) ∃x (EcoFriendly(x)) ∀x (UsedIn(x, tomsHouse) → Disposable(x) ⊕ Reusable(x)) ∀x (MadeFrom(x, metal) → ¬MadeFrom(x, plastic)) ∀x (Reusable(x) → MadeFrom(x, metal)) ¬(MadeFrom(chopsticksUsedInTomsHouse, metal) ⊕ MadeFrom(chopsticksUsedInTomsHouse, plastic))

The chopsticks used in Tom's house are eco-friendly.

EcoFriendly(chopsticks)

Uncertain

All disposables are designed to be used only once. Some items used in Tom's house are eco-friendly. Every item used in Tom's house is either disposable or reusable. If something is made from metal, then it is not made from plastic. All reusable items used in Tom's house are made from metal. The chopsticks used in Tom's house are either made from metals and plastics, or that they are neither made from metals nor plastics.

∀x (Disposable(x) → DesignedToBeOnlyUsedOnce(x)) ∃x (EcoFriendly(x)) ∀x (UsedIn(x, tomsHouse) → Disposable(x) ⊕ Reusable(x)) ∀x (MadeFrom(x, metal) → ¬MadeFrom(x, plastic)) ∀x (Reusable(x) → MadeFrom(x, metal)) ¬(MadeFrom(chopsticksUsedInTomsHouse, metal) ⊕ MadeFrom(chopsticksUsedInTomsHouse, plastic))

The chopsticks used in Tom's house are eco-friendly or designed to be used only once.

EcoFriendly(chopsticks) ∨ DesignedToBeOnlyUsedOnce(chopsticks)

True

All disposables are designed to be used only once. Some items used in Tom's house are eco-friendly. Every item used in Tom's house is either disposable or reusable. If something is made from metal, then it is not made from plastic. All reusable items used in Tom's house are made from metal. The chopsticks used in Tom's house are either made from metals and plastics, or that they are neither made from metals nor plastics.

∀x (Disposable(x) → DesignedToBeOnlyUsedOnce(x)) ∃x (EcoFriendly(x)) ∀x (UsedIn(x, tomsHouse) → Disposable(x) ⊕ Reusable(x)) ∀x (MadeFrom(x, metal) → ¬MadeFrom(x, plastic)) ∀x (Reusable(x) → MadeFrom(x, metal)) ¬(MadeFrom(chopsticksUsedInTomsHouse, metal) ⊕ MadeFrom(chopsticksUsedInTomsHouse, plastic))

If chopsticks used in Tom's house are made from plastic or designed to be used only once, then they are made from plastic and are eco-friendly.

MadeFrom(chopsticks, plastic) ∨ DesignedBeOnlyUsedOnce(chopsticks) → MadeFrom(chopsticks, plastic) ∧ EcoFriendly(chopsticks)

False

Anything lazy is unproductive. No one unproductive is energetic. If something is a sloth, then it is lazy. Some animals are sloths. Sid is neither an energetic person nor a sloth.

∀x (Lazy(x) → Unproductive(x)) ∀x (Unproductive(x) → ¬Energetic(x)) ∀x (Sloth(x) → Lazy(x)) ∃x (Animal(x) ∧ Sloth(x)) ¬Energetic(sid) ∧ ¬Sloth(sid))

Sid is an animal.

Animal(sid)

Uncertain

Anything lazy is unproductive. No one unproductive is energetic. If something is a sloth, then it is lazy. Some animals are sloths. Sid is neither an energetic person nor a sloth.

∀x (Lazy(x) → Unproductive(x)) ∀x (Unproductive(x) → ¬Energetic(x)) ∀x (Sloth(x) → Lazy(x)) ∃x (Animal(x) ∧ Sloth(x)) ¬Energetic(sid) ∧ ¬Sloth(sid))

Sid is an energetic person and an animal.

Energetic(sid) ∧ Animal(sid)

False

Anything lazy is unproductive. No one unproductive is energetic. If something is a sloth, then it is lazy. Some animals are sloths. Sid is neither an energetic person nor a sloth.

∀x (Lazy(x) → Unproductive(x)) ∀x (Unproductive(x) → ¬Energetic(x)) ∀x (Sloth(x) → Lazy(x)) ∃x (Animal(x) ∧ Sloth(x)) ¬Energetic(sid) ∧ ¬Sloth(sid))

If Sid is either an animal or unproductive, then Sid is not an energetic person.

Animal(sid) ⊕ Unproductive(sid)) → ¬Energetic(sid)

True

European soccer clubs can attend UCL, UEL, and UECL. A soccer club eligible to attend UCL has a higher ranking than a soccer club eligible to attend UEL. A soccer club eligible to attend UEL has a higher ranking than a soccer club eligible to attend UECL. Manchester United and Machester City are both European soccer clubs. Manchester United is eligible to attend UEL next season. Manchester City is eligible to attend UCL next season.

∀x (EuropeanSoccerClub(x) → Attend(x, ucl) ∨ Attend(x, uel) ∨ Attend(x, uecl)) ∀x ∀y (EuropeanSoccerClub(x) ∧ EuropeanSoccerClub(y) ∧ Attend(x, ucl) ∧ Attend(y, uel) → HigherRank(x, y)) ∀x ∀y (EuropeanSoccerClub(x) ∧ EuropeanSoccerClub(y) ∧ Attend(x, uel) ∧ Attend(y, uecl) → HigherRank(x, y)) EuropeanSoccerClub(manchesterUnited) ∧ EuropeanSoccerClub(manchesterCity) Attend(manchesterunited, uel) Attend(manchestercity, ucl)

Manchester City has a higher ranking than Manchester United.

HigherRank(manchesterCity, manchesterUnited)

True

If a person coaches a football club, the person is a football coach. If a person has a position in a club in a year, and the club is in NFL in the same year, the person plays in NFL. Minnesota Vikings is a football club. Dennis Green coached Minnesota Vikings. Cris Carter had 13 touchdown receptions. Minnesota Vikings were in the National Football League in 1997. John Randle was Minnesota Vikings defensive tackle in 1997.

∀x ∀y ((Coach(x, y) ∧ FootballClub(y)) → FootballCoach(x)) ∀w ∀x ∀y ∀z ((PlayPositionFor(x, w, y, z) ∧ InNFL(y, z)) → PlayInNFL(x)) FootballClub(minnesotaVikings) Coach(dennisGreen, minnesotaVikings) ReceiveTD(crisCarter, num13) InNFL(minnesotaVikings, yr1997) PlayPositionFor(johnRandle, defensiveTackle, minnesotaVikings, yr1997)

Dennis Green is a football coach.

FootballCoach(dennisGreen)

True

If a person coaches a football club, the person is a football coach. If a person has a position in a club in a year, and the club is in NFL in the same year, the person plays in NFL. Minnesota Vikings is a football club. Dennis Green coached Minnesota Vikings. Cris Carter had 13 touchdown receptions. Minnesota Vikings were in the National Football League in 1997. John Randle was Minnesota Vikings defensive tackle in 1997.

∀x ∀y ((Coach(x, y) ∧ FootballClub(y)) → FootballCoach(x)) ∀w ∀x ∀y ∀z ((PlayPositionFor(x, w, y, z) ∧ InNFL(y, z)) → PlayInNFL(x)) FootballClub(minnesotaVikings) Coach(dennisGreen, minnesotaVikings) ReceiveTD(crisCarter, num13) InNFL(minnesotaVikings, yr1997) PlayPositionFor(johnRandle, defensiveTackle, minnesotaVikings, yr1997)

John Randle didn't play in the National Football League.

¬PlayInNFL(johnRandle)

False

If a person coaches a football club, the person is a football coach. If a person has a position in a club in a year, and the club is in NFL in the same year, the person plays in NFL. Minnesota Vikings is a football club. Dennis Green coached Minnesota Vikings. Cris Carter had 13 touchdown receptions. Minnesota Vikings were in the National Football League in 1997. John Randle was Minnesota Vikings defensive tackle in 1997.

∀x ∀y ((Coach(x, y) ∧ FootballClub(y)) → FootballCoach(x)) ∀w ∀x ∀y ∀z ((PlayPositionFor(x, w, y, z) ∧ InNFL(y, z)) → PlayInNFL(x)) FootballClub(minnesotaVikings) Coach(dennisGreen, minnesotaVikings) ReceiveTD(crisCarter, num13) InNFL(minnesotaVikings, yr1997) PlayPositionFor(johnRandle, defensiveTackle, minnesotaVikings, yr1997)

Cris Carter played for Minnesota Vikings.

PlayPositionFor(crisCarter, wr, minnesotaVikings, year1997)

Uncertain

All classrooms in William L. Harkness Hall that are used for lectures are booked during the day. None of the classrooms in William L. Harkness Hall are private study spots. All classrooms in William L. Harkness Hall are used for lectures or used for office hours. If a classroom in William L. Harkness Hall is booked in the evening, then it is not freely usable at night. If a classroom in William L. Harkness Hall is used for office hours, then it is booked in the evening. Room 116 is a classroom in William L. Harkness Hall that is either both used for lecture and used for office hours or not used for either.

∀x (ClassroomIn(x, williamLHarknessHall) ∧ UsedFor(x, lecture) → BookedDuring(x, day)) ∀x (ClassroomIn(x, williamLHarknessHall) ∧ ¬PrivateStudySpot(x)) ∀x (ClassroomIn(x, williamLHarknessHall) ∧ (UsedFor(x, lecture) ∨ UsedFor(x, officeHours))) ∀x (ClassroomIn(x, williamLHarknessHall) ∧ BookedIn(x, evening) → ¬FreelyUsableAtNight(x)) ∀x (ClassroomIn(x, williamLHarknessHall) ∧ UsedFor(x, officeHours) → BookedIn(x, evening)) ClassroomIn(116, williamLHarknessHall) ∧ ¬(UsedFor(116, lecture) ⊕ UsedFor(116, officeHours))

Room 116 is a private study spot.

PrivateStudySpot(room116)

False

All classrooms in William L. Harkness Hall that are used for lectures are booked during the day. None of the classrooms in William L. Harkness Hall are private study spots. All classrooms in William L. Harkness Hall are used for lectures or used for office hours. If a classroom in William L. Harkness Hall is booked in the evening, then it is not freely usable at night. If a classroom in William L. Harkness Hall is used for office hours, then it is booked in the evening. Room 116 is a classroom in William L. Harkness Hall that is either both used for lecture and used for office hours or not used for either.

∀x (ClassroomIn(x, williamLHarknessHall) ∧ UsedFor(x, lecture) → BookedDuring(x, day)) ∀x (ClassroomIn(x, williamLHarknessHall) ∧ ¬PrivateStudySpot(x)) ∀x (ClassroomIn(x, williamLHarknessHall) ∧ (UsedFor(x, lecture) ∨ UsedFor(x, officeHours))) ∀x (ClassroomIn(x, williamLHarknessHall) ∧ BookedIn(x, evening) → ¬FreelyUsableAtNight(x)) ∀x (ClassroomIn(x, williamLHarknessHall) ∧ UsedFor(x, officeHours) → BookedIn(x, evening)) ClassroomIn(116, williamLHarknessHall) ∧ ¬(UsedFor(116, lecture) ⊕ UsedFor(116, officeHours))

If Room 116 is either both booked during the day and freely usable at night, or neither, then it is either used for office hours or for private study spots.

¬(BookedDuring(room116, day) ⊕ FreelyUsableAtNight(room116) → (UsedFor(room116, officeHour) ⊕ PrivateStudySpot(room116))

True

All classrooms in William L. Harkness Hall that are used for lectures are booked during the day. None of the classrooms in William L. Harkness Hall are private study spots. All classrooms in William L. Harkness Hall are used for lectures or used for office hours. If a classroom in William L. Harkness Hall is booked in the evening, then it is not freely usable at night. If a classroom in William L. Harkness Hall is used for office hours, then it is booked in the evening. Room 116 is a classroom in William L. Harkness Hall that is either both used for lecture and used for office hours or not used for either.

∀x (ClassroomIn(x, williamLHarknessHall) ∧ UsedFor(x, lecture) → BookedDuring(x, day)) ∀x (ClassroomIn(x, williamLHarknessHall) ∧ ¬PrivateStudySpot(x)) ∀x (ClassroomIn(x, williamLHarknessHall) ∧ (UsedFor(x, lecture) ∨ UsedFor(x, officeHours))) ∀x (ClassroomIn(x, williamLHarknessHall) ∧ BookedIn(x, evening) → ¬FreelyUsableAtNight(x)) ∀x (ClassroomIn(x, williamLHarknessHall) ∧ UsedFor(x, officeHours) → BookedIn(x, evening)) ClassroomIn(116, williamLHarknessHall) ∧ ¬(UsedFor(116, lecture) ⊕ UsedFor(116, officeHours))

If Room 116 is not both a private study spot and freely useable at night, then it is either used for lectures or booked during the day.

¬(PrivateStudySpot(room116) ∧ FreelyUsableAtNight(room116)) → (UsedFor(room116, lecture) ∨ BookedIn(room116, evening))

False

Shafaq-Asiman is a large complex of offshore geological structures in the Caspian Sea. Baku is northwest of Shafaq-Asiman. If place A is northwest of place B, then place B is southeast of place A.

LargeComplex(shafaq-asiman) ∧ LargeComplex(shafaq-asiman) ∧ Offshore(shafaq-asiman) ∧ GeologicalStructures(shafaq-asiman) ∧ In(shafaq-asiman, caspiansea) NorthwestOf(baku, shafaq-asiman) ∀x ∀y (NorthwestOf(x, y) → SoutheastOf(y, x))

Baku is southeast of Shafaq-Asiman.

SoutheastOf(baku, shafaq-asiman)

Uncertain

Shafaq-Asiman is a large complex of offshore geological structures in the Caspian Sea. Baku is northwest of Shafaq-Asiman. If place A is northwest of place B, then place B is southeast of place A.

LargeComplex(shafaq-asiman) ∧ LargeComplex(shafaq-asiman) ∧ Offshore(shafaq-asiman) ∧ GeologicalStructures(shafaq-asiman) ∧ In(shafaq-asiman, caspiansea) NorthwestOf(baku, shafaq-asiman) ∀x ∀y (NorthwestOf(x, y) → SoutheastOf(y, x))

A large complex is southeast of Baku.

∃x (LargeComplex(x) ∧ SoutheastOf(x, baku))

True

Shafaq-Asiman is a large complex of offshore geological structures in the Caspian Sea. Baku is northwest of Shafaq-Asiman. If place A is northwest of place B, then place B is southeast of place A.

LargeComplex(shafaq-asiman) ∧ LargeComplex(shafaq-asiman) ∧ Offshore(shafaq-asiman) ∧ GeologicalStructures(shafaq-asiman) ∧ In(shafaq-asiman, caspiansea) NorthwestOf(baku, shafaq-asiman) ∀x ∀y (NorthwestOf(x, y) → SoutheastOf(y, x))

Baku is not northwest of offshore geological structures.

∀x (GeologicalStructures(x) ∧ Offshore(x) → ¬NorthwestOf(baku, x))

False

Herodicus was a Greek physician, dietician, sophist, and gymnast. Herodicus was born in the city of Selymbria. Selymbria is a colony of the city-state Megara. One of the tutors of Hippocrates was Herodicus. Massages were recommended by Herodicus. Some of the theories of Herodicus are considered to be the foundation of sports medicine.

Greek(herodicus) ∧ Physician(herodicus) ∧ Dietician(herodicus) ∧ Sophist(herodicus) ∧ Gymnast(herodicus) Born(herodicus, selymbia) ∧ City(selymbia) Colony(selymbia, megara) ∧ CityState(megara) Tutor(herodicus, hippocrates) Recommend(herodicus, massages) ∃x ∃y (Theory(x) ∧ From(x, herodicus) ∧ FoundationOf(x, sportsMedicine) ∧ (¬(x=y)) ∧ Theory(y) ∧ From(y, herodicus) ∧ FoundationOf(y, sportsMedicine))

Herodicus tutored Hippocrates.

Tutor(herodicus, hippocrates)

True

Herodicus was a Greek physician, dietician, sophist, and gymnast. Herodicus was born in the city of Selymbria. Selymbria is a colony of the city-state Megara. One of the tutors of Hippocrates was Herodicus. Massages were recommended by Herodicus. Some of the theories of Herodicus are considered to be the foundation of sports medicine.

Greek(herodicus) ∧ Physician(herodicus) ∧ Dietician(herodicus) ∧ Sophist(herodicus) ∧ Gymnast(herodicus) Born(herodicus, selymbia) ∧ City(selymbia) Colony(selymbia, megara) ∧ CityState(megara) Tutor(herodicus, hippocrates) Recommend(herodicus, massages) ∃x ∃y (Theory(x) ∧ From(x, herodicus) ∧ FoundationOf(x, sportsMedicine) ∧ (¬(x=y)) ∧ Theory(y) ∧ From(y, herodicus) ∧ FoundationOf(y, sportsMedicine))

Herodicus was tutored by Hippocrates.

Tutor(hippocrates, herodicus)

Uncertain

Herodicus was a Greek physician, dietician, sophist, and gymnast. Herodicus was born in the city of Selymbria. Selymbria is a colony of the city-state Megara. One of the tutors of Hippocrates was Herodicus. Massages were recommended by Herodicus. Some of the theories of Herodicus are considered to be the foundation of sports medicine.

Greek(herodicus) ∧ Physician(herodicus) ∧ Dietician(herodicus) ∧ Sophist(herodicus) ∧ Gymnast(herodicus) Born(herodicus, selymbia) ∧ City(selymbia) Colony(selymbia, megara) ∧ CityState(megara) Tutor(herodicus, hippocrates) Recommend(herodicus, massages) ∃x ∃y (Theory(x) ∧ From(x, herodicus) ∧ FoundationOf(x, sportsMedicine) ∧ (¬(x=y)) ∧ Theory(y) ∧ From(y, herodicus) ∧ FoundationOf(y, sportsMedicine))

Herodicus was born in a city-state.

∃x (Born(herodicus, x) ∧ CityState(x))

Uncertain

Herodicus was a Greek physician, dietician, sophist, and gymnast. Herodicus was born in the city of Selymbria. Selymbria is a colony of the city-state Megara. One of the tutors of Hippocrates was Herodicus. Massages were recommended by Herodicus. Some of the theories of Herodicus are considered to be the foundation of sports medicine.

Greek(herodicus) ∧ Physician(herodicus) ∧ Dietician(herodicus) ∧ Sophist(herodicus) ∧ Gymnast(herodicus) Born(herodicus, selymbia) ∧ City(selymbia) Colony(selymbia, megara) ∧ CityState(megara) Tutor(herodicus, hippocrates) Recommend(herodicus, massages) ∃x ∃y (Theory(x) ∧ From(x, herodicus) ∧ FoundationOf(x, sportsMedicine) ∧ (¬(x=y)) ∧ Theory(y) ∧ From(y, herodicus) ∧ FoundationOf(y, sportsMedicine))

Herodicus did not recommend massages.

¬Recommend(herodicus, massages)

False

Herodicus was a Greek physician, dietician, sophist, and gymnast. Herodicus was born in the city of Selymbria. Selymbria is a colony of the city-state Megara. One of the tutors of Hippocrates was Herodicus. Massages were recommended by Herodicus. Some of the theories of Herodicus are considered to be the foundation of sports medicine.

Greek(herodicus) ∧ Physician(herodicus) ∧ Dietician(herodicus) ∧ Sophist(herodicus) ∧ Gymnast(herodicus) Born(herodicus, selymbia) ∧ City(selymbia) Colony(selymbia, megara) ∧ CityState(megara) Tutor(herodicus, hippocrates) Recommend(herodicus, massages) ∃x ∃y (Theory(x) ∧ From(x, herodicus) ∧ FoundationOf(x, sportsMedicine) ∧ (¬(x=y)) ∧ Theory(y) ∧ From(y, herodicus) ∧ FoundationOf(y, sportsMedicine))

Herodicus was born in a colony of a city-state.

∃x ∃y (Born(herodicus, x) ∧ Colony(x, y) ∧ CityState(y))

True

None of the kids in our family love the opera. All of the adults in our family love the opera. If someone in our family is a scientist, then they are an adult. Some students in our family are kids. Billy is a kid in our family.

∀x ((Kid(x) ∧ In(x, ourFamily)) → ¬Love(x, opera)) ∀x ((Adult(x) ∧ In(x, ourFamily)) → Love(x, opera)) ∀x ((Scientist(x) ∧ In(x, ourFamily)) → Adult(x)) ∃x (Student(x) ∧ In(x, ourFamily) ∧ Kid(x)) Kid(billy) ∧ In(billy, ourFamily)

Billy is a student.

Student(billy)

Uncertain

None of the kids in our family love the opera. All of the adults in our family love the opera. If someone in our family is a scientist, then they are an adult. Some students in our family are kids. Billy is a kid in our family.

∀x ((Kid(x) ∧ In(x, ourFamily)) → ¬Love(x, opera)) ∀x ((Adult(x) ∧ In(x, ourFamily)) → Love(x, opera)) ∀x ((Scientist(x) ∧ In(x, ourFamily)) → Adult(x)) ∃x (Student(x) ∧ In(x, ourFamily) ∧ Kid(x)) Kid(billy) ∧ In(billy, ourFamily)

Billy is a student and a scientist.

Student(billy) ∧ Scientist(billy)

False

None of the kids in our family love the opera. All of the adults in our family love the opera. If someone in our family is a scientist, then they are an adult. Some students in our family are kids. Billy is a kid in our family.

∀x ((Kid(x) ∧ In(x, ourFamily)) → ¬Love(x, opera)) ∀x ((Adult(x) ∧ In(x, ourFamily)) → Love(x, opera)) ∀x ((Scientist(x) ∧ In(x, ourFamily)) → Adult(x)) ∃x (Student(x) ∧ In(x, ourFamily) ∧ Kid(x)) Kid(billy) ∧ In(billy, ourFamily)

If Billy is a student or a scientist, then Billy is a student and a kid.

(Student(billy) ∨ Scientist(billy)) → (Student(billy) ∧ Kid(billy))

True

Brian Winter is a Scottish football referee. After being injured, Brian Winter retired in 2012. Brian Winter was appointed as a referee observer after his retirement. Some football referees become referee observers. The son of Brian Winter, Andy Winter, is a football player who plays for Hamilton Academical.

Scottish(brianWinter) ∧ FootballReferee(brianWinter) Retired(brianWinter) ∧ RetiredIn(brianWinter, yr2012) RefereeObserver(brianWinter) ∃x (FootballReferee(x) ∧ RefereeObserver(x)) SonOf(andyWinter, brianWinter) ∧ FootballPlayer(andyWinter) ∧ PlaysFor(andyWinter, hamiltonAcademical)

There is a son of a referee observer that plays football.

∃x ∃y(SonOf(x, y) ∧ RefereeObserver(y) ∧ FootballPlayer(x))

True

Brian Winter is a Scottish football referee. After being injured, Brian Winter retired in 2012. Brian Winter was appointed as a referee observer after his retirement. Some football referees become referee observers. The son of Brian Winter, Andy Winter, is a football player who plays for Hamilton Academical.

Scottish(brianWinter) ∧ FootballReferee(brianWinter) Retired(brianWinter) ∧ RetiredIn(brianWinter, yr2012) RefereeObserver(brianWinter) ∃x (FootballReferee(x) ∧ RefereeObserver(x)) SonOf(andyWinter, brianWinter) ∧ FootballPlayer(andyWinter) ∧ PlaysFor(andyWinter, hamiltonAcademical)

Brian Winter was not a referee observer.

¬RefereeObserver(brianwinter)

False

Brian Winter is a Scottish football referee. After being injured, Brian Winter retired in 2012. Brian Winter was appointed as a referee observer after his retirement. Some football referees become referee observers. The son of Brian Winter, Andy Winter, is a football player who plays for Hamilton Academical.

Scottish(brianWinter) ∧ FootballReferee(brianWinter) Retired(brianWinter) ∧ RetiredIn(brianWinter, yr2012) RefereeObserver(brianWinter) ∃x (FootballReferee(x) ∧ RefereeObserver(x)) SonOf(andyWinter, brianWinter) ∧ FootballPlayer(andyWinter) ∧ PlaysFor(andyWinter, hamiltonAcademical)

Brian Winter is retired.

Retired(brianwinter)

True

Brian Winter is a Scottish football referee. After being injured, Brian Winter retired in 2012. Brian Winter was appointed as a referee observer after his retirement. Some football referees become referee observers. The son of Brian Winter, Andy Winter, is a football player who plays for Hamilton Academical.

Scottish(brianWinter) ∧ FootballReferee(brianWinter) Retired(brianWinter) ∧ RetiredIn(brianWinter, yr2012) RefereeObserver(brianWinter) ∃x (FootballReferee(x) ∧ RefereeObserver(x)) SonOf(andyWinter, brianWinter) ∧ FootballPlayer(andyWinter) ∧ PlaysFor(andyWinter, hamiltonAcademical)

Andy Winter is a referee.

Referee(andywinter)

Uncertain

Everyone at 'Board Game night' is interested in puzzles, or they are bad at chess, or both. If a person at 'Board Game night' is bad at chess, then they don't play a lot of chess. There is a person at 'Board Game night' who is either a planner or a creative person. Erica is at 'Board Game night,' and she is someone who plays a lot of chess. If Erica is neither bad at chess nor creative, then Erica is either someone who plans and is creative, or she is neither of these things.

∀x (At(x, boardGameNight) → (InterestedIn(x, puzzle) ∨ BadAt(x, chess))) ∀x ((At(x, boardGameNight) ∧ BadAt(x, chess)) → ¬PlaysOften(x, chess)) ∃x (At(x, boardGameNight) ∧ (Planner(x) ∨ Creative(x))) At(erica, boardGameNight) ∧ PlaysOften(erica, chess) (At(erica, boardGameNight) ∧ (¬(BadAt(erica, chess) ∨ Creative(erica)))) → ¬(Planner(erica) ⊕ Creative(erica))

Erica plans.

Planner(erica)

Uncertain

Everyone at 'Board Game night' is interested in puzzles, or they are bad at chess, or both. If a person at 'Board Game night' is bad at chess, then they don't play a lot of chess. There is a person at 'Board Game night' who is either a planner or a creative person. Erica is at 'Board Game night,' and she is someone who plays a lot of chess. If Erica is neither bad at chess nor creative, then Erica is either someone who plans and is creative, or she is neither of these things.

∀x (At(x, boardGameNight) → (InterestedIn(x, puzzle) ∨ BadAt(x, chess))) ∀x ((At(x, boardGameNight) ∧ BadAt(x, chess)) → ¬PlaysOften(x, chess)) ∃x (At(x, boardGameNight) ∧ (Planner(x) ∨ Creative(x))) At(erica, boardGameNight) ∧ PlaysOften(erica, chess) (At(erica, boardGameNight) ∧ (¬(BadAt(erica, chess) ∨ Creative(erica)))) → ¬(Planner(erica) ⊕ Creative(erica))

Erica is interested in puzzles and is creative.

InterestedIn(erica, puzzle) ∧ Creative(erica)

True

Everyone at 'Board Game night' is interested in puzzles, or they are bad at chess, or both. If a person at 'Board Game night' is bad at chess, then they don't play a lot of chess. There is a person at 'Board Game night' who is either a planner or a creative person. Erica is at 'Board Game night,' and she is someone who plays a lot of chess. If Erica is neither bad at chess nor creative, then Erica is either someone who plans and is creative, or she is neither of these things.

∀x (At(x, boardGameNight) → (InterestedIn(x, puzzle) ∨ BadAt(x, chess))) ∀x ((At(x, boardGameNight) ∧ BadAt(x, chess)) → ¬PlaysOften(x, chess)) ∃x (At(x, boardGameNight) ∧ (Planner(x) ∨ Creative(x))) At(erica, boardGameNight) ∧ PlaysOften(erica, chess) (At(erica, boardGameNight) ∧ (¬(BadAt(erica, chess) ∨ Creative(erica)))) → ¬(Planner(erica) ⊕ Creative(erica))

Erica is either interested in puzzles or is creative.

InterestedIn(erica, puzzle) ⊕ Creative(erica)

False

Everyone at 'Board Game night' is interested in puzzles, or they are bad at chess, or both. If a person at 'Board Game night' is bad at chess, then they don't play a lot of chess. There is a person at 'Board Game night' who is either a planner or a creative person. Erica is at 'Board Game night,' and she is someone who plays a lot of chess. If Erica is neither bad at chess nor creative, then Erica is either someone who plans and is creative, or she is neither of these things.

∀x (At(x, boardGameNight) → (InterestedIn(x, puzzle) ∨ BadAt(x, chess))) ∀x ((At(x, boardGameNight) ∧ BadAt(x, chess)) → ¬PlaysOften(x, chess)) ∃x (At(x, boardGameNight) ∧ (Planner(x) ∨ Creative(x))) At(erica, boardGameNight) ∧ PlaysOften(erica, chess) (At(erica, boardGameNight) ∧ (¬(BadAt(erica, chess) ∨ Creative(erica)))) → ¬(Planner(erica) ⊕ Creative(erica))

If Erica plans ahead or plays a lot of chess matches, then Erica is not interested in puzzles and creative.

Planner(erica) ∨ PlaysOften(erica, chess))) → (¬(InterestedIn(erica, puzzle) ∧ Creative(erica))

False

Everyone at 'Board Game night' is interested in puzzles, or they are bad at chess, or both. If a person at 'Board Game night' is bad at chess, then they don't play a lot of chess. There is a person at 'Board Game night' who is either a planner or a creative person. Erica is at 'Board Game night,' and she is someone who plays a lot of chess. If Erica is neither bad at chess nor creative, then Erica is either someone who plans and is creative, or she is neither of these things.

∀x (At(x, boardGameNight) → (InterestedIn(x, puzzle) ∨ BadAt(x, chess))) ∀x ((At(x, boardGameNight) ∧ BadAt(x, chess)) → ¬PlaysOften(x, chess)) ∃x (At(x, boardGameNight) ∧ (Planner(x) ∨ Creative(x))) At(erica, boardGameNight) ∧ PlaysOften(erica, chess) (At(erica, boardGameNight) ∧ (¬(BadAt(erica, chess) ∨ Creative(erica)))) → ¬(Planner(erica) ⊕ Creative(erica))

If Erica is creative, then Erica is not interested in puzzles and creative.

Creative(erica)) → (¬(InterestedIn(erica, puzzle) ∧ Creative(erica))

False

Everyone at 'Board Game night' is interested in puzzles, or they are bad at chess, or both. If a person at 'Board Game night' is bad at chess, then they don't play a lot of chess. There is a person at 'Board Game night' who is either a planner or a creative person. Erica is at 'Board Game night,' and she is someone who plays a lot of chess. If Erica is neither bad at chess nor creative, then Erica is either someone who plans and is creative, or she is neither of these things.

∀x (At(x, boardGameNight) → (InterestedIn(x, puzzle) ∨ BadAt(x, chess))) ∀x ((At(x, boardGameNight) ∧ BadAt(x, chess)) → ¬PlaysOften(x, chess)) ∃x (At(x, boardGameNight) ∧ (Planner(x) ∨ Creative(x))) At(erica, boardGameNight) ∧ PlaysOften(erica, chess) (At(erica, boardGameNight) ∧ (¬(BadAt(erica, chess) ∨ Creative(erica)))) → ¬(Planner(erica) ⊕ Creative(erica))

If Erica is interested in puzzles and is creative, then Erica is not creative.

InterestedIn(erica, puzzle) ∧ Creative(erica)) → ¬Creative(erica)

False

Everyone at 'Board Game night' is interested in puzzles, or they are bad at chess, or both. If a person at 'Board Game night' is bad at chess, then they don't play a lot of chess. There is a person at 'Board Game night' who is either a planner or a creative person. Erica is at 'Board Game night,' and she is someone who plays a lot of chess. If Erica is neither bad at chess nor creative, then Erica is either someone who plans and is creative, or she is neither of these things.

∀x (At(x, boardGameNight) → (InterestedIn(x, puzzle) ∨ BadAt(x, chess))) ∀x ((At(x, boardGameNight) ∧ BadAt(x, chess)) → ¬PlaysOften(x, chess)) ∃x (At(x, boardGameNight) ∧ (Planner(x) ∨ Creative(x))) At(erica, boardGameNight) ∧ PlaysOften(erica, chess) (At(erica, boardGameNight) ∧ (¬(BadAt(erica, chess) ∨ Creative(erica)))) → ¬(Planner(erica) ⊕ Creative(erica))

If Erica either plays a lot of chess matches or is creative, then Erica is neither interested in puzzles nor a person who plays a lot of chess matches.

PlaysOften(erica, chess) ⊕ InterestedIn(erica, puzzle) → ¬(InterestedIn(erica, puzzle) ∨ PlaysOften(erica, chess))

True

Everyone at 'Board Game night' is interested in puzzles, or they are bad at chess, or both. If a person at 'Board Game night' is bad at chess, then they don't play a lot of chess. There is a person at 'Board Game night' who is either a planner or a creative person. Erica is at 'Board Game night,' and she is someone who plays a lot of chess. If Erica is neither bad at chess nor creative, then Erica is either someone who plans and is creative, or she is neither of these things.

∀x (At(x, boardGameNight) → (InterestedIn(x, puzzle) ∨ BadAt(x, chess))) ∀x ((At(x, boardGameNight) ∧ BadAt(x, chess)) → ¬PlaysOften(x, chess)) ∃x (At(x, boardGameNight) ∧ (Planner(x) ∨ Creative(x))) At(erica, boardGameNight) ∧ PlaysOften(erica, chess) (At(erica, boardGameNight) ∧ (¬(BadAt(erica, chess) ∨ Creative(erica)))) → ¬(Planner(erica) ⊕ Creative(erica))

If Erica is interested in puzzles and plays a lot of chess matches, then Erica is either a person who plays a lot of chess matches or a person that is creative.

PlaysOften(erica, chess) ⊕ InterestedIn(erica, puzzle)) → ¬(InterestedIn(erica, puzzle) ∨ PlaysOften(erica, chess)

False

Everyone at 'Board Game night' is interested in puzzles, or they are bad at chess, or both. If a person at 'Board Game night' is bad at chess, then they don't play a lot of chess. There is a person at 'Board Game night' who is either a planner or a creative person. Erica is at 'Board Game night,' and she is someone who plays a lot of chess. If Erica is neither bad at chess nor creative, then Erica is either someone who plans and is creative, or she is neither of these things.

∀x (At(x, boardGameNight) → (InterestedIn(x, puzzle) ∨ BadAt(x, chess))) ∀x ((At(x, boardGameNight) ∧ BadAt(x, chess)) → ¬PlaysOften(x, chess)) ∃x (At(x, boardGameNight) ∧ (Planner(x) ∨ Creative(x))) At(erica, boardGameNight) ∧ PlaysOften(erica, chess) (At(erica, boardGameNight) ∧ (¬(BadAt(erica, chess) ∨ Creative(erica)))) → ¬(Planner(erica) ⊕ Creative(erica))

If Erica plans ahead or is interested in puzzles, then Erica is creative.

Planner(erica) ∨ InterestedIn(erica, puzzle) → Creative(erica)

True

Everyone at 'Board Game night' is interested in puzzles, or they are bad at chess, or both. If a person at 'Board Game night' is bad at chess, then they don't play a lot of chess. There is a person at 'Board Game night' who is either a planner or a creative person. Erica is at 'Board Game night,' and she is someone who plays a lot of chess. If Erica is neither bad at chess nor creative, then Erica is either someone who plans and is creative, or she is neither of these things.

∀x (At(x, boardGameNight) → (InterestedIn(x, puzzle) ∨ BadAt(x, chess))) ∀x ((At(x, boardGameNight) ∧ BadAt(x, chess)) → ¬PlaysOften(x, chess)) ∃x (At(x, boardGameNight) ∧ (Planner(x) ∨ Creative(x))) At(erica, boardGameNight) ∧ PlaysOften(erica, chess) (At(erica, boardGameNight) ∧ (¬(BadAt(erica, chess) ∨ Creative(erica)))) → ¬(Planner(erica) ⊕ Creative(erica))

If Erica is either bad at chess or interested in puzzles, then Erica is not a person who plays a lot of chess matches and creative.

BadAt(erica, chess) ⊕ InterestedIn(erica, puzzle) → ¬(PlaysOften(erica, chess) ∧ Creative(erica))

False

Soccer players have a right foot and a left foot. Top soccer players are soccer players who can use both the left foot and right foot very efficiently. If a soccer player can score many goals using the left foot, they can use that foot very efficiently. If a soccer player can score many goals using the right foot, they can use that foot very efficiently. Cristiano Ronaldo is a soccer player. Cristiano Ronaldo can use his right foot very efficiently. Cristiano Ronaldo has scored many goals using his left foot.

∀x (SoccerPlayer(x) → Have(x, leftFoot) ∧ Have(x, rightFoot)) ∀x (SoccerPlayer(x) ∧ UseEfficiently(x, leftFoot) ∧ UseEfficiently(x, rightFoot) → TopSoccerPlayer(x)) ∀x (SoccerPlayer(x) ∧ ScoreUsing(x, manyGoals, leftFoot) → UseEfficiently(x, leftFoot)) ∀x (SoccerPlayer(x) ∧ ScoreUsing(x, manyGoals, rightFoot) → UseEfficiently(x, rightFoot)) SoccerPlayer(ronaldo) UseEfficiently(ronaldo, rightFoot) ScoreUsing(ronaldo, manyGoals, leftFoot)

Cristiano Ronaldo is a top soccer player.

TopSoccerPlayer(ronaldo)

True

Soccer players have a right foot and a left foot. Top soccer players are soccer players who can use both the left foot and right foot very efficiently. If a soccer player can score many goals using the left foot, they can use that foot very efficiently. If a soccer player can score many goals using the right foot, they can use that foot very efficiently. Cristiano Ronaldo is a soccer player. Cristiano Ronaldo can use his right foot very efficiently. Cristiano Ronaldo has scored many goals using his left foot.

∀x (SoccerPlayer(x) → Have(x, leftFoot) ∧ Have(x, rightFoot)) ∀x (SoccerPlayer(x) ∧ UseEfficiently(x, leftFoot) ∧ UseEfficiently(x, rightFoot) → TopSoccerPlayer(x)) ∀x (SoccerPlayer(x) ∧ ScoreUsing(x, manyGoals, leftFoot) → UseEfficiently(x, leftFoot)) ∀x (SoccerPlayer(x) ∧ ScoreUsing(x, manyGoals, rightFoot) → UseEfficiently(x, rightFoot)) SoccerPlayer(ronaldo) UseEfficiently(ronaldo, rightFoot) ScoreUsing(ronaldo, manyGoals, leftFoot)

Cristiano Ronaldo is not a top soccer player.

¬TopSoccerPlayer(ronaldo)

False

The National Lobster Hatchery is a hatchery located in Padstow, England. The National Lobster Hatchery is open to visitors. A hatchery is either for profit or for conservation. If a hatchery is for conservation, it might release animals into the wild. The National Lobster Hatchery is not for profit.

Hatchery(nationalLobsterHatchery) ∧ LocatedIn(nationalLobsterHatchery, padstowEngland) OpenToVisitor(nationalLobsterHatchery) ∀x (Hatchery(x) → ForConservation(x) ⊕ ForProfit(x)) ∃x (Hatchery(x) ∧ ForConservation(x) ∧ ReleaseAnimalToWild(x)) ¬ForProfit(nationalLobsterHatchery)

The National Lobster Hatchery is for conservation.

ForConservation(nationalLobsterhatchery)

True

The National Lobster Hatchery is a hatchery located in Padstow, England. The National Lobster Hatchery is open to visitors. A hatchery is either for profit or for conservation. If a hatchery is for conservation, it might release animals into the wild. The National Lobster Hatchery is not for profit.

Hatchery(nationalLobsterHatchery) ∧ LocatedIn(nationalLobsterHatchery, padstowEngland) OpenToVisitor(nationalLobsterHatchery) ∀x (Hatchery(x) → ForConservation(x) ⊕ ForProfit(x)) ∃x (Hatchery(x) ∧ ForConservation(x) ∧ ReleaseAnimalToWild(x)) ¬ForProfit(nationalLobsterHatchery)

All hatcheries are open to visitors.

∀x (Hatchery(x) → OpenToVisitors(x))

Uncertain

The National Lobster Hatchery is a hatchery located in Padstow, England. The National Lobster Hatchery is open to visitors. A hatchery is either for profit or for conservation. If a hatchery is for conservation, it might release animals into the wild. The National Lobster Hatchery is not for profit.

Hatchery(nationalLobsterHatchery) ∧ LocatedIn(nationalLobsterHatchery, padstowEngland) OpenToVisitor(nationalLobsterHatchery) ∀x (Hatchery(x) → ForConservation(x) ⊕ ForProfit(x)) ∃x (Hatchery(x) ∧ ForConservation(x) ∧ ReleaseAnimalToWild(x)) ¬ForProfit(nationalLobsterHatchery)

The National Lobster Hatchery releases animals into the wild.

ReleaseAnimalToWild(nationalLobsterhatchery)

Uncertain

Rhos Aelwyd F.C. is a Welsh football club. Rhos Aelwyd F.C. is the only football club located in Ponciau. The Premier Division was won in June 2005 by a team from Ponciau. The winner of the Premier Division in October 2009 was promoted to the Cymru Alliance. The Premier Division in October 2009 was won by the same team that won in June 2005.

∀x (Rhosaelwydfc(x) → FootballClub(x) ∧ Welsh(x)) ∀x (FootballClub(x) ∧ LocatedIn(x, ponciau) ↔ Rhosaelwydfc(x)) ∃x (LocatedIn(x, ponciau) ∧ WonPremierDivisionDuring(x, year2005MonthJune)) ∀x (WonPremierDivisionDuring(x, year2009MonthOctober) → PromotedTo(x, cymruAlliance)) ∀x (WonPremierDivisionDuring(x, year2009MonthOctober) ↔ WonPremierDivisionDuring(x, y2005MonthJune))

Rhos Aelwyd F.C. won Premier Division in June 2005.

∃x (Rhosaelwydfc(x) ∧ WonPremierDivisionDuring(x, year2005MonthJune))

True

Rhos Aelwyd F.C. is a Welsh football club. Rhos Aelwyd F.C. is the only football club located in Ponciau. The Premier Division was won in June 2005 by a team from Ponciau. The winner of the Premier Division in October 2009 was promoted to the Cymru Alliance. The Premier Division in October 2009 was won by the same team that won in June 2005.

∀x (Rhosaelwydfc(x) → FootballClub(x) ∧ Welsh(x)) ∀x (FootballClub(x) ∧ LocatedIn(x, ponciau) ↔ Rhosaelwydfc(x)) ∃x (LocatedIn(x, ponciau) ∧ WonPremierDivisionDuring(x, year2005MonthJune)) ∀x (WonPremierDivisionDuring(x, year2009MonthOctober) → PromotedTo(x, cymruAlliance)) ∀x (WonPremierDivisionDuring(x, year2009MonthOctober) ↔ WonPremierDivisionDuring(x, y2005MonthJune))

Rhos Aelwyd F.C. was promoted to the Cymru Alliance.

∃x (Rhosaelwydfc(x) ∧ PromotedTo(x, cymruAlliance))

True

A Unix operating system used in the lab computers is a piece of software. All versions of MacOS used in the lab computer are based on Unix operating systems. A lab computer uses either MacOS or Linux. All Linux computers in the lab are convenient. All software used in the lab computers is written with code. If something is convenient in the lab computer, then it is popular. Burger is used in the lab computer, and it is written with code and a new version of MacOS. PyTorch is used in the lab computer, and PyTorch is neither a Linux system nor a piece of software.

∀x (UsedIn(x, labComputer) ∧ UnixOperatingSystem(x) → Software(x)) ∀x (UsedIn(x, labComputer) ∧ MacOS(x) → UnixOperatingSystem(x)) ∀x (UsedIn(x, labComputer) → MacOS(x) ⊕ Linux(x)) ∀x (UsedIn(x, labComputer) ∧ Linux(x) → Convenient(x)) ∀x (UsedIn(x, labComputer) ∧ Software(x) → WrittenWithCode(x)) ∀x (UsedIn(x, labComputer) ∧ Convenient(x) → Popular(x)) UsedIn(burger, labComputer) ∧ WrittenWithCode(burger) ∧ MacOS(burger)) UsedIn(pytorch, labComputer) ∧ ¬(Linux(pytorch) ⊕ Software(pytorch))

Burger is popular.

Popular(burger)

Uncertain

A Unix operating system used in the lab computers is a piece of software. All versions of MacOS used in the lab computer are based on Unix operating systems. A lab computer uses either MacOS or Linux. All Linux computers in the lab are convenient. All software used in the lab computers is written with code. If something is convenient in the lab computer, then it is popular. Burger is used in the lab computer, and it is written with code and a new version of MacOS. PyTorch is used in the lab computer, and PyTorch is neither a Linux system nor a piece of software.

∀x (UsedIn(x, labComputer) ∧ UnixOperatingSystem(x) → Software(x)) ∀x (UsedIn(x, labComputer) ∧ MacOS(x) → UnixOperatingSystem(x)) ∀x (UsedIn(x, labComputer) → MacOS(x) ⊕ Linux(x)) ∀x (UsedIn(x, labComputer) ∧ Linux(x) → Convenient(x)) ∀x (UsedIn(x, labComputer) ∧ Software(x) → WrittenWithCode(x)) ∀x (UsedIn(x, labComputer) ∧ Convenient(x) → Popular(x)) UsedIn(burger, labComputer) ∧ WrittenWithCode(burger) ∧ MacOS(burger)) UsedIn(pytorch, labComputer) ∧ ¬(Linux(pytorch) ⊕ Software(pytorch))

Burger is not popular.

¬Popular(burger)

Uncertain

A Unix operating system used in the lab computers is a piece of software. All versions of MacOS used in the lab computer are based on Unix operating systems. A lab computer uses either MacOS or Linux. All Linux computers in the lab are convenient. All software used in the lab computers is written with code. If something is convenient in the lab computer, then it is popular. Burger is used in the lab computer, and it is written with code and a new version of MacOS. PyTorch is used in the lab computer, and PyTorch is neither a Linux system nor a piece of software.

∀x (UsedIn(x, labComputer) ∧ UnixOperatingSystem(x) → Software(x)) ∀x (UsedIn(x, labComputer) ∧ MacOS(x) → UnixOperatingSystem(x)) ∀x (UsedIn(x, labComputer) → MacOS(x) ⊕ Linux(x)) ∀x (UsedIn(x, labComputer) ∧ Linux(x) → Convenient(x)) ∀x (UsedIn(x, labComputer) ∧ Software(x) → WrittenWithCode(x)) ∀x (UsedIn(x, labComputer) ∧ Convenient(x) → Popular(x)) UsedIn(burger, labComputer) ∧ WrittenWithCode(burger) ∧ MacOS(burger)) UsedIn(pytorch, labComputer) ∧ ¬(Linux(pytorch) ⊕ Software(pytorch))

PyTorch is popular and written with code.

Popular(pytorch) ∧ WrittenWithCode(pytorch)

True

A Unix operating system used in the lab computers is a piece of software. All versions of MacOS used in the lab computer are based on Unix operating systems. A lab computer uses either MacOS or Linux. All Linux computers in the lab are convenient. All software used in the lab computers is written with code. If something is convenient in the lab computer, then it is popular. Burger is used in the lab computer, and it is written with code and a new version of MacOS. PyTorch is used in the lab computer, and PyTorch is neither a Linux system nor a piece of software.

∀x (UsedIn(x, labComputer) ∧ UnixOperatingSystem(x) → Software(x)) ∀x (UsedIn(x, labComputer) ∧ MacOS(x) → UnixOperatingSystem(x)) ∀x (UsedIn(x, labComputer) → MacOS(x) ⊕ Linux(x)) ∀x (UsedIn(x, labComputer) ∧ Linux(x) → Convenient(x)) ∀x (UsedIn(x, labComputer) ∧ Software(x) → WrittenWithCode(x)) ∀x (UsedIn(x, labComputer) ∧ Convenient(x) → Popular(x)) UsedIn(burger, labComputer) ∧ WrittenWithCode(burger) ∧ MacOS(burger)) UsedIn(pytorch, labComputer) ∧ ¬(Linux(pytorch) ⊕ Software(pytorch))

PyTorch is not popular and it is not written with code.

¬(Popular(pytorch) ∧ WrittenWithCode(pytorch))

False

Roads are made of either concrete or asphalt. Roads made of concrete last longer than roads made with asphalt. Roads made of asphalt are smoother than roads made of concrete. Everyone prefers the smoother of two roads. The first road is made of concrete, and the second road is made of asphalt.

∀x (Road(x) → (MadeOf(x, concrete) ⊕ MadeOf(x, asphalt)) ∀x ∀y (Road(x) ∧ MadeOf(x, concrete) ∧ Road(y) ∧ MadeOf(y, asphalt) → LastLonger(x, y)) ∀x ∀y (Road(x) ∧ MadeOf(x, asphalt) ∧ Road(y) ∧ MadeOf(y, concrete) → Smoother(x, y)) ∀x ∀y ∀z (Road(x) ∧ Road(y) ∧ Smoother(x, y) → Prefer(z, x)) Road(firstRoad) ∧ MadeOf(secondRoad, concrete) ∧ Road(firstRoad) ∧ MadeOf(secondRoad, asphalt)

The first road will last longer than the second road.

LastLonger(firstRoad, secondRoad)

True

Roads are made of either concrete or asphalt. Roads made of concrete last longer than roads made with asphalt. Roads made of asphalt are smoother than roads made of concrete. Everyone prefers the smoother of two roads. The first road is made of concrete, and the second road is made of asphalt.

∀x (Road(x) → (MadeOf(x, concrete) ⊕ MadeOf(x, asphalt)) ∀x ∀y (Road(x) ∧ MadeOf(x, concrete) ∧ Road(y) ∧ MadeOf(y, asphalt) → LastLonger(x, y)) ∀x ∀y (Road(x) ∧ MadeOf(x, asphalt) ∧ Road(y) ∧ MadeOf(y, concrete) → Smoother(x, y)) ∀x ∀y ∀z (Road(x) ∧ Road(y) ∧ Smoother(x, y) → Prefer(z, x)) Road(firstRoad) ∧ MadeOf(secondRoad, concrete) ∧ Road(firstRoad) ∧ MadeOf(secondRoad, asphalt)

The second road is not smoother than the first one.

¬Smoother(firstRoad, secondRoad)

False

Roads are made of either concrete or asphalt. Roads made of concrete last longer than roads made with asphalt. Roads made of asphalt are smoother than roads made of concrete. Everyone prefers the smoother of two roads. The first road is made of concrete, and the second road is made of asphalt.

∀x (Road(x) → (MadeOf(x, concrete) ⊕ MadeOf(x, asphalt)) ∀x ∀y (Road(x) ∧ MadeOf(x, concrete) ∧ Road(y) ∧ MadeOf(y, asphalt) → LastLonger(x, y)) ∀x ∀y (Road(x) ∧ MadeOf(x, asphalt) ∧ Road(y) ∧ MadeOf(y, concrete) → Smoother(x, y)) ∀x ∀y ∀z (Road(x) ∧ Road(y) ∧ Smoother(x, y) → Prefer(z, x)) Road(firstRoad) ∧ MadeOf(secondRoad, concrete) ∧ Road(firstRoad) ∧ MadeOf(secondRoad, asphalt)

John prefers the second road.

Prefer(john, secondRoad)

True

Camp Davern is a traditional summer camp for boys and girls. Camp Davern was established in the year 1946. Camp Davern was operated by the YMCA until the year 2015. Camp Davern is an old summer camp.

TraditionalSummerCamp(campDavern) ∧ ForBoysAndGirls(campDavern) EstablishedIn(campDavern, year1946) OperatedUntil(yMCA, campDavern, year2015) Old(campDavern)

One of Ontario's oldest summer camps is a traditional summer camp for boys and girls.

∃x (Old(x) ∧ TraditionalSummerCamp(x) ∧ ForBoysAndGirls(x))

True

Camp Davern is a traditional summer camp for boys and girls. Camp Davern was established in the year 1946. Camp Davern was operated by the YMCA until the year 2015. Camp Davern is an old summer camp.

TraditionalSummerCamp(campDavern) ∧ ForBoysAndGirls(campDavern) EstablishedIn(campDavern, year1946) OperatedUntil(yMCA, campDavern, year2015) Old(campDavern)

A traditional summer camp for boys and girls was operated by the YMCA until the year 2015.

∃x (TraditionalSummerCamp(x) ∧ ForBoysAndGirls(x) ∧ OperatedUntil(YMCA, x, year2015))

True

Camp Davern is a traditional summer camp for boys and girls. Camp Davern was established in the year 1946. Camp Davern was operated by the YMCA until the year 2015. Camp Davern is an old summer camp.

TraditionalSummerCamp(campDavern) ∧ ForBoysAndGirls(campDavern) EstablishedIn(campDavern, year1946) OperatedUntil(yMCA, campDavern, year2015) Old(campDavern)

Camp Davern was established in 1989.

EstablishedIn(campdavern, year1989)

Uncertain

If Emily's friends publish journals, then they do not work in the entertainment industry. All of Emily's friends who are award-winning novelists publish journals. Emily's friends work in the entertainment industry or are highly acclaimed in their profession. If Emily's friends are highly acclaimed in their profession, then they often hold tenured and high-ranking positions at their workplace. If Emily's friends are highly acclaimed in their profession, then they often receive glowing feedback and recommendations from their colleagues. Taylor is Emily's friend. It is not true that Taylor both holds highly acclaimed in her profession and often holds tenured and high-ranking positions at her workplace.

∀x (EmilysFriend(x) ∧ Publish(x, journal) → ¬WorkIn(x, entertainmentIndustry)) ∀x (EmilysFriend(x) ∧ AwardWinningNovelist(x) → Publish(x, journal)) ∀x (EmilysFriend(x) → WorkIn(x, entertainmentIndustry) ∨ HighlyAcclaimedIn(x, theirProfession)) ∀x (EmilysFriend(x) ∧ HighlyAcclaimedIn(x, theirProfession) → ∃y (HoldAt(x, y, workPlace) ∧ Tenured(y) ∧ HighRanking(y) ∧ Position(y))) ∀x (EmilysFriend(x) ∧ HighlyAcclaimedIn(x, theirProfession) → ReceiveFrom(x, glowingFeedback, colleague) ∧ ReceiveFrom(x, glowingRecommendation, colleague)) EmilysFriends(taylor) ¬(HighlyAcclaimedIn(taylor, theirProfession) ∧ (∃y (HoldAt(taylor, y, workPlace) ∧ Tenured(y) ∧ HighRanking(y) ∧ Position(y)))

Taylor is Emily's friend and she often holds tenured and high-ranking positions at her workplace.

EmilysFriends(taylor) ∧ (∃y (HoldAt(taylor, y, workPlace) ∧ Tenured(y) ∧ HighRanking(y) ∧ Position(y)))

Uncertain

If Emily's friends publish journals, then they do not work in the entertainment industry. All of Emily's friends who are award-winning novelists publish journals. Emily's friends work in the entertainment industry or are highly acclaimed in their profession. If Emily's friends are highly acclaimed in their profession, then they often hold tenured and high-ranking positions at their workplace. If Emily's friends are highly acclaimed in their profession, then they often receive glowing feedback and recommendations from their colleagues. Taylor is Emily's friend. It is not true that Taylor both holds highly acclaimed in her profession and often holds tenured and high-ranking positions at her workplace.

∀x (EmilysFriend(x) ∧ Publish(x, journal) → ¬WorkIn(x, entertainmentIndustry)) ∀x (EmilysFriend(x) ∧ AwardWinningNovelist(x) → Publish(x, journal)) ∀x (EmilysFriend(x) → WorkIn(x, entertainmentIndustry) ∨ HighlyAcclaimedIn(x, theirProfession)) ∀x (EmilysFriend(x) ∧ HighlyAcclaimedIn(x, theirProfession) → ∃y (HoldAt(x, y, workPlace) ∧ Tenured(y) ∧ HighRanking(y) ∧ Position(y))) ∀x (EmilysFriend(x) ∧ HighlyAcclaimedIn(x, theirProfession) → ReceiveFrom(x, glowingFeedback, colleague) ∧ ReceiveFrom(x, glowingRecommendation, colleague)) EmilysFriends(taylor) ¬(HighlyAcclaimedIn(taylor, theirProfession) ∧ (∃y (HoldAt(taylor, y, workPlace) ∧ Tenured(y) ∧ HighRanking(y) ∧ Position(y)))

Taylor is Emily's friend and she often receives glowing feedback and recommendations from their colleagues and is an award-winning novelist.

EmilysFriends(taylor) ∧ (Receive(taylor, glowingFeedback, colleague) ∧ Receive(taylor, glowingRecommendation, colleague) ∧ AwardWinningNovelist(taylor))

False

If Emily's friends publish journals, then they do not work in the entertainment industry. All of Emily's friends who are award-winning novelists publish journals. Emily's friends work in the entertainment industry or are highly acclaimed in their profession. If Emily's friends are highly acclaimed in their profession, then they often hold tenured and high-ranking positions at their workplace. If Emily's friends are highly acclaimed in their profession, then they often receive glowing feedback and recommendations from their colleagues. Taylor is Emily's friend. It is not true that Taylor both holds highly acclaimed in her profession and often holds tenured and high-ranking positions at her workplace.

∀x (EmilysFriend(x) ∧ Publish(x, journal) → ¬WorkIn(x, entertainmentIndustry)) ∀x (EmilysFriend(x) ∧ AwardWinningNovelist(x) → Publish(x, journal)) ∀x (EmilysFriend(x) → WorkIn(x, entertainmentIndustry) ∨ HighlyAcclaimedIn(x, theirProfession)) ∀x (EmilysFriend(x) ∧ HighlyAcclaimedIn(x, theirProfession) → ∃y (HoldAt(x, y, workPlace) ∧ Tenured(y) ∧ HighRanking(y) ∧ Position(y))) ∀x (EmilysFriend(x) ∧ HighlyAcclaimedIn(x, theirProfession) → ReceiveFrom(x, glowingFeedback, colleague) ∧ ReceiveFrom(x, glowingRecommendation, colleague)) EmilysFriends(taylor) ¬(HighlyAcclaimedIn(taylor, theirProfession) ∧ (∃y (HoldAt(taylor, y, workPlace) ∧ Tenured(y) ∧ HighRanking(y) ∧ Position(y)))

Taylor is Emily's friend and she does not both publish journals and is an award-winning novelist.

EmilysFriends(taylor) ∧ ¬(Publish(taylor, journal) ∧ AwardWinningNovelist(taylor))

True

Thick as Thieves is a young adult fantasy novel written by Megan Whalen Turner. Thick as Thieves was published by Greenwillow Books. If a book was published by a company, then the author of that book worked with the company that published the book. The fictional Mede Empire is where Thick as Thieves is set. The Mede Empire plots to swallow up some nearby countries. Attolia and Sounis are countries near the Mede Empire. Thick as Thieves was sold both as a hardcover and an e-book.

YoungAdultFantasy(thickAsTheives) ∧ Novel(thickAsTheives) ∧ WrittenBy(thickAsTheives, meganWhalenTurner) PublishedBy(thickAsTheives, greenWillowBooks) ∀x ∀y ∀z ((WrittenBy(x, y) ∧ PublishedBy(x, z)) → WorkedWith(y, z)) Fictional(medeEmpire) ∧ SetIn(thickAsTheives, medeEmpire) ∃x ∃y ((Country(x) ∧ Near(x, medeEmpire) ∧ PlotsToSwallowUp(medeEmpire, x)) ∧ (¬(x=y) ∧ Near(y, medeEmpire) ∧ PlotsToSwallowUp(medeEmpire, y))) Country(attolia) ∧ Near(attolia, medeEmpire) ∧ Country(sounis) ∧ Near(sounis, medeEmpire) SoldAs(thickAsTheives, hardCover) ∧ SoldAs(thickAsTheives, softCover)

Megan Whalen Turner worked with Greenwillow Books.

WorkedWith(WhalenTurner, greenWillowbooks)

True

Thick as Thieves is a young adult fantasy novel written by Megan Whalen Turner. Thick as Thieves was published by Greenwillow Books. If a book was published by a company, then the author of that book worked with the company that published the book. The fictional Mede Empire is where Thick as Thieves is set. The Mede Empire plots to swallow up some nearby countries. Attolia and Sounis are countries near the Mede Empire. Thick as Thieves was sold both as a hardcover and an e-book.

YoungAdultFantasy(thickAsTheives) ∧ Novel(thickAsTheives) ∧ WrittenBy(thickAsTheives, meganWhalenTurner) PublishedBy(thickAsTheives, greenWillowBooks) ∀x ∀y ∀z ((WrittenBy(x, y) ∧ PublishedBy(x, z)) → WorkedWith(y, z)) Fictional(medeEmpire) ∧ SetIn(thickAsTheives, medeEmpire) ∃x ∃y ((Country(x) ∧ Near(x, medeEmpire) ∧ PlotsToSwallowUp(medeEmpire, x)) ∧ (¬(x=y) ∧ Near(y, medeEmpire) ∧ PlotsToSwallowUp(medeEmpire, y))) Country(attolia) ∧ Near(attolia, medeEmpire) ∧ Country(sounis) ∧ Near(sounis, medeEmpire) SoldAs(thickAsTheives, hardCover) ∧ SoldAs(thickAsTheives, softCover)

The Mede Empire plans to swallow up Attolia.

PlotsToSwallowUp(medeEmpire, attolia)

Uncertain

Thick as Thieves is a young adult fantasy novel written by Megan Whalen Turner. Thick as Thieves was published by Greenwillow Books. If a book was published by a company, then the author of that book worked with the company that published the book. The fictional Mede Empire is where Thick as Thieves is set. The Mede Empire plots to swallow up some nearby countries. Attolia and Sounis are countries near the Mede Empire. Thick as Thieves was sold both as a hardcover and an e-book.

YoungAdultFantasy(thickAsTheives) ∧ Novel(thickAsTheives) ∧ WrittenBy(thickAsTheives, meganWhalenTurner) PublishedBy(thickAsTheives, greenWillowBooks) ∀x ∀y ∀z ((WrittenBy(x, y) ∧ PublishedBy(x, z)) → WorkedWith(y, z)) Fictional(medeEmpire) ∧ SetIn(thickAsTheives, medeEmpire) ∃x ∃y ((Country(x) ∧ Near(x, medeEmpire) ∧ PlotsToSwallowUp(medeEmpire, x)) ∧ (¬(x=y) ∧ Near(y, medeEmpire) ∧ PlotsToSwallowUp(medeEmpire, y))) Country(attolia) ∧ Near(attolia, medeEmpire) ∧ Country(sounis) ∧ Near(sounis, medeEmpire) SoldAs(thickAsTheives, hardCover) ∧ SoldAs(thickAsTheives, softCover)

Thick as Thieves is not set in the Mede Empire.

¬SetIn(thickAsTheives, medeEmpire)

False

Thick as Thieves is a young adult fantasy novel written by Megan Whalen Turner. Thick as Thieves was published by Greenwillow Books. If a book was published by a company, then the author of that book worked with the company that published the book. The fictional Mede Empire is where Thick as Thieves is set. The Mede Empire plots to swallow up some nearby countries. Attolia and Sounis are countries near the Mede Empire. Thick as Thieves was sold both as a hardcover and an e-book.

YoungAdultFantasy(thickAsTheives) ∧ Novel(thickAsTheives) ∧ WrittenBy(thickAsTheives, meganWhalenTurner) PublishedBy(thickAsTheives, greenWillowBooks) ∀x ∀y ∀z ((WrittenBy(x, y) ∧ PublishedBy(x, z)) → WorkedWith(y, z)) Fictional(medeEmpire) ∧ SetIn(thickAsTheives, medeEmpire) ∃x ∃y ((Country(x) ∧ Near(x, medeEmpire) ∧ PlotsToSwallowUp(medeEmpire, x)) ∧ (¬(x=y) ∧ Near(y, medeEmpire) ∧ PlotsToSwallowUp(medeEmpire, y))) Country(attolia) ∧ Near(attolia, medeEmpire) ∧ Country(sounis) ∧ Near(sounis, medeEmpire) SoldAs(thickAsTheives, hardCover) ∧ SoldAs(thickAsTheives, softCover)

Megan Whalen Turner did not work with Greenwillow Books.

¬WorkedWith(megan, greenWillowbooks)

False

WeTab is a MeeGo-based tablet computer. WeTab was announced by Neofonie. Neofonie is a German producer. Germans live in Germany or abroad.

MeeGoBased(weTab) ∧ TabletComputer(weTab) ∀x (AnnouncedBy(weTab, neofonie)) German(neofonie) ∧ Producer(neofonie) ∀x (German(x) → LiveIn(x, german) ⊕ LiveAbroad(x))

There is a tablet computer announced by a German producer.

∃x ∃y (TabletComputer(x) ∧ German(y) ∧ Producer(y) ∧ AnnouncedBy(x, y))

True

WeTab is a MeeGo-based tablet computer. WeTab was announced by Neofonie. Neofonie is a German producer. Germans live in Germany or abroad.

MeeGoBased(weTab) ∧ TabletComputer(weTab) ∀x (AnnouncedBy(weTab, neofonie)) German(neofonie) ∧ Producer(neofonie) ∀x (German(x) → LiveIn(x, german) ⊕ LiveAbroad(x))

Neofonie doesn't speak English or German.

¬Speak(neofonie, english) ∧ ¬Speak(neofonie, german)

False

Some employees in James's town who work in business analysis are good at math. All of the employees in James's town who work in business analysis are working for this company. None of the employees in James's town who work for this company are from China. All of the employees in James's town working in software engineering are from China. Leif is an employee in James's town, and he is working in software engineering.

∃x ∃y (EmployeeIn(x, jamesSTown) ∧ WorkIn(x, businessAnalysis) ∧ GoodAt(x, math) ∧ (¬(x=y)) ∧ EmployeeIn(y, jamesSTown) ∧ WorkIn(y, businessAnalysis) ∧ GoodAt(y, math)) ∀x ((EmployeeIn(x, jamesSTown) ∧ WorkIn(x, businessAnalysis)) → WorkFor(x, thisCompany)) ∀x ((EmployeeIn(x, jamesSTown) ∧ WorkFor(x, thisCompany)) → ¬From(x, china)) ∀x (EmployeeIn(x, jamesSTown) ∧ WorkIn(x, softwareEngineering) → From(x, china)) EmployeeIn(leif, jamesSTown) ∧ WorkIn(leif, softwareEngineering)

Leif is good at math.

EmployeesInJamesSTown(leif) ∧ GoodAt(leif, math)

Uncertain

Some employees in James's town who work in business analysis are good at math. All of the employees in James's town who work in business analysis are working for this company. None of the employees in James's town who work for this company are from China. All of the employees in James's town working in software engineering are from China. Leif is an employee in James's town, and he is working in software engineering.

∃x ∃y (EmployeeIn(x, jamesSTown) ∧ WorkIn(x, businessAnalysis) ∧ GoodAt(x, math) ∧ (¬(x=y)) ∧ EmployeeIn(y, jamesSTown) ∧ WorkIn(y, businessAnalysis) ∧ GoodAt(y, math)) ∀x ((EmployeeIn(x, jamesSTown) ∧ WorkIn(x, businessAnalysis)) → WorkFor(x, thisCompany)) ∀x ((EmployeeIn(x, jamesSTown) ∧ WorkFor(x, thisCompany)) → ¬From(x, china)) ∀x (EmployeeIn(x, jamesSTown) ∧ WorkIn(x, softwareEngineering) → From(x, china)) EmployeeIn(leif, jamesSTown) ∧ WorkIn(leif, softwareEngineering)

Leif is not both good at math and working in business analysis.

¬(GoodAt(leif, math) ∧ WorkIn(leif, businessAnalysis))

False

Some employees in James's town who work in business analysis are good at math. All of the employees in James's town who work in business analysis are working for this company. None of the employees in James's town who work for this company are from China. All of the employees in James's town working in software engineering are from China. Leif is an employee in James's town, and he is working in software engineering.

∃x ∃y (EmployeeIn(x, jamesSTown) ∧ WorkIn(x, businessAnalysis) ∧ GoodAt(x, math) ∧ (¬(x=y)) ∧ EmployeeIn(y, jamesSTown) ∧ WorkIn(y, businessAnalysis) ∧ GoodAt(y, math)) ∀x ((EmployeeIn(x, jamesSTown) ∧ WorkIn(x, businessAnalysis)) → WorkFor(x, thisCompany)) ∀x ((EmployeeIn(x, jamesSTown) ∧ WorkFor(x, thisCompany)) → ¬From(x, china)) ∀x (EmployeeIn(x, jamesSTown) ∧ WorkIn(x, softwareEngineering) → From(x, china)) EmployeeIn(leif, jamesSTown) ∧ WorkIn(leif, softwareEngineering)

If Leif is not both good at math and in business analysis, then he is neither working in this company nor working in software engineering.

¬(GoodAt(leif, math) ∧ WorkIn(leif, businessAnalysis)) → (¬WorkFor(x, thisCompany) ∧ ¬WorkIn(x, softwareEngineering))

True

The party provides five kinds of fruits: strawberry, orange, blueberry, grape, and cherry. If the fruit had the lowest remaining weight at the end of the party, then it means it was the most popular fruit. At the end of the party, strawberries had the lowest remaining weight. At the end of the party, the number of leftover blueberries was lower than that of cherries. Benjamin only ate oranges and grapes at the party.

Provide(party, strawberry) ∧ Provide(party, orange) ∧ Provide(party, blueberry) ∧ Provide(party, grape) ∧ Provide(party, cherry) ∀x (LowestWeightRemainingAt(x, endOfParty) → MostPopular(x)) LowestWeightRemainingAt(strawberries, endOfParty) LowerWeightAt(blueberry, cherry, endOfParty) Eat(benjamin, orange) ∧ Eat(benjamin, grape) ∧ ¬Eat(benjamin, blueberry) ∧ ¬Eat(benjamin, cherry) ∧ ¬Eat(benjamin, strawberry)

Blueberries were the most popular fruit at the party.

MostPopular(blueberry)

Uncertain

The party provides five kinds of fruits: strawberry, orange, blueberry, grape, and cherry. If the fruit had the lowest remaining weight at the end of the party, then it means it was the most popular fruit. At the end of the party, strawberries had the lowest remaining weight. At the end of the party, the number of leftover blueberries was lower than that of cherries. Benjamin only ate oranges and grapes at the party.

Provide(party, strawberry) ∧ Provide(party, orange) ∧ Provide(party, blueberry) ∧ Provide(party, grape) ∧ Provide(party, cherry) ∀x (LowestWeightRemainingAt(x, endOfParty) → MostPopular(x)) LowestWeightRemainingAt(strawberries, endOfParty) LowerWeightAt(blueberry, cherry, endOfParty) Eat(benjamin, orange) ∧ Eat(benjamin, grape) ∧ ¬Eat(benjamin, blueberry) ∧ ¬Eat(benjamin, cherry) ∧ ¬Eat(benjamin, strawberry)

Cherries were the most popular fruit at the party.

MostPopular(cherry)

Uncertain

The party provides five kinds of fruits: strawberry, orange, blueberry, grape, and cherry. If the fruit had the lowest remaining weight at the end of the party, then it means it was the most popular fruit. At the end of the party, strawberries had the lowest remaining weight. At the end of the party, the number of leftover blueberries was lower than that of cherries. Benjamin only ate oranges and grapes at the party.

Provide(party, strawberry) ∧ Provide(party, orange) ∧ Provide(party, blueberry) ∧ Provide(party, grape) ∧ Provide(party, cherry) ∀x (LowestWeightRemainingAt(x, endOfParty) → MostPopular(x)) LowestWeightRemainingAt(strawberries, endOfParty) LowerWeightAt(blueberry, cherry, endOfParty) Eat(benjamin, orange) ∧ Eat(benjamin, grape) ∧ ¬Eat(benjamin, blueberry) ∧ ¬Eat(benjamin, cherry) ∧ ¬Eat(benjamin, strawberry)

Benjamin ate blueberries at the party.

Eat(blueberry, benjamin)

False

All students who attend in person have registered for the conference. Students either attend the conference in person or remotely. No students from China attend the conference remotely. James attends the conference, but he does not attend the conference remotely. Jack attends the conference, and he is a student from China.

∀x (AttendInPerson(x) → Registered(x)) ∀x (Attend(x) → (AttendInPerson(x) ⊕ AttendRemotely(x))) ∀x ((Attend(x) ∧ FromChina(x)) → ¬AttendRemotely(x)) Attend(james) ∧ (¬AttendRemotely(james)) FromChina(jack) ∧ Attend(jack)

James attends the conference but not in person.

Attend(james) ∧ (¬AttendInPerson(james))

False

All students who attend in person have registered for the conference. Students either attend the conference in person or remotely. No students from China attend the conference remotely. James attends the conference, but he does not attend the conference remotely. Jack attends the conference, and he is a student from China.

∀x (AttendInPerson(x) → Registered(x)) ∀x (Attend(x) → (AttendInPerson(x) ⊕ AttendRemotely(x))) ∀x ((Attend(x) ∧ FromChina(x)) → ¬AttendRemotely(x)) Attend(james) ∧ (¬AttendRemotely(james)) FromChina(jack) ∧ Attend(jack)

Jack attends the conference in person.

Attend(jack) ∧ AttendInPerson(jack)

True

All students who attend in person have registered for the conference. Students either attend the conference in person or remotely. No students from China attend the conference remotely. James attends the conference, but he does not attend the conference remotely. Jack attends the conference, and he is a student from China.

∀x (AttendInPerson(x) → Registered(x)) ∀x (Attend(x) → (AttendInPerson(x) ⊕ AttendRemotely(x))) ∀x ((Attend(x) ∧ FromChina(x)) → ¬AttendRemotely(x)) Attend(james) ∧ (¬AttendRemotely(james)) FromChina(jack) ∧ Attend(jack)

Jack has registered for the conference.

Registered(jack)

True

David Ha'ivri is a political strategist. If you are born in Israel to at least one Israeli parent, you receive Israeli citizenship at birth. David Ha'ivri emigrated to the United States from Israel, where he was born to Israeli parents. Several Zionist leaders have been elected to the Shomron Regional Municipal council. David Ha'ivri is a Zionist leader.

PoliticalStrategist(davidHaivri) ∀x ∃y (BornInIsrael(x) ∧ ParentOf(y, x) ∧ Israeli(y) → Israeli(x)) ∃x (EmigratedTo(davidHaivri, america) ∧ BornInIsrael(davidHaivri) ∧ ParentOf(davidHaivri, x) ∧ Israeli(x)) ∃x (ZionistLeader(x) ∧ ElectedTo(x, shomronMunicipalCouncil)) ZionstLeader(davidHaivri)

David Ha'ivri is an Israeli citizen.

IsraeliCitizen(davidHaivri)

True

David Ha'ivri is a political strategist. If you are born in Israel to at least one Israeli parent, you receive Israeli citizenship at birth. David Ha'ivri emigrated to the United States from Israel, where he was born to Israeli parents. Several Zionist leaders have been elected to the Shomron Regional Municipal council. David Ha'ivri is a Zionist leader.

PoliticalStrategist(davidHaivri) ∀x ∃y (BornInIsrael(x) ∧ ParentOf(y, x) ∧ Israeli(y) → Israeli(x)) ∃x (EmigratedTo(davidHaivri, america) ∧ BornInIsrael(davidHaivri) ∧ ParentOf(davidHaivri, x) ∧ Israeli(x)) ∃x (ZionistLeader(x) ∧ ElectedTo(x, shomronMunicipalCouncil)) ZionstLeader(davidHaivri)

David Ha'ivri is a United States citizen.

American(davidHaivri)

Uncertain

David Ha'ivri is a political strategist. If you are born in Israel to at least one Israeli parent, you receive Israeli citizenship at birth. David Ha'ivri emigrated to the United States from Israel, where he was born to Israeli parents. Several Zionist leaders have been elected to the Shomron Regional Municipal council. David Ha'ivri is a Zionist leader.

PoliticalStrategist(davidHaivri) ∀x ∃y (BornInIsrael(x) ∧ ParentOf(y, x) ∧ Israeli(y) → Israeli(x)) ∃x (EmigratedTo(davidHaivri, america) ∧ BornInIsrael(davidHaivri) ∧ ParentOf(davidHaivri, x) ∧ Israeli(x)) ∃x (ZionistLeader(x) ∧ ElectedTo(x, shomronMunicipalCouncil)) ZionstLeader(davidHaivri)

David Ha'ivri has been elected to the Shomron Regional Municipal council.

ElectedTo(davidHaivri, shomronMunicipalCouncil)

Uncertain

Mary has the flu. If someone has the flu, then they have influenza. Susan doesn't have influenza.

Has(mary, flu) ∀x (Has(x, flu) → Has(x, influenza)) ¬Has(susan, influenza)

Either Mary or Susan has influenza.

Has(mary, influenza) ⊕ Has(susan, influenza)

True

James Cocks was a British lawyer. James Cocks was a Whig politician who sat in the House of Commons. A British is a European. Any lawyer is familiar with laws. Some Whigs speak French.

British(james) ∧ Lawyer(james) Whig(james) ∧ Politician(james) ∧ SatInHouseOfCommons(james) ∀x (British(x) → European(x)) ∀x (Lawyer(x) → FamiliarWithLaws(x)) ∃x ∃y (Whig(x) ∧ SpeakFrench(x)) ∧ (¬(x=y)) ∧ (Whig(y) ∧ SpeakFrench(y))

No lawyer ever sat in the House of Commons.

∀x (Lawyer(x) → ¬SatInHouseOfCommons(x))

False

James Cocks was a British lawyer. James Cocks was a Whig politician who sat in the House of Commons. A British is a European. Any lawyer is familiar with laws. Some Whigs speak French.

British(james) ∧ Lawyer(james) Whig(james) ∧ Politician(james) ∧ SatInHouseOfCommons(james) ∀x (British(x) → European(x)) ∀x (Lawyer(x) → FamiliarWithLaws(x)) ∃x ∃y (Whig(x) ∧ SpeakFrench(x)) ∧ (¬(x=y)) ∧ (Whig(y) ∧ SpeakFrench(y))

Some European was familiar with laws.

∃x (European(x) ∧ FamiliarWithLaws(x))

True

James Cocks was a British lawyer. James Cocks was a Whig politician who sat in the House of Commons. A British is a European. Any lawyer is familiar with laws. Some Whigs speak French.

British(james) ∧ Lawyer(james) Whig(james) ∧ Politician(james) ∧ SatInHouseOfCommons(james) ∀x (British(x) → European(x)) ∀x (Lawyer(x) → FamiliarWithLaws(x)) ∃x ∃y (Whig(x) ∧ SpeakFrench(x)) ∧ (¬(x=y)) ∧ (Whig(y) ∧ SpeakFrench(y))

James Cocks speaks French.

SpeakFrench(james)

Uncertain

Beasts of Prey is a fantasy novel or a science fiction novel, or both. Science fiction novels are not about mythological creatures Beasts of Prey Is about a creature known as the Shetani. Shetanis are mythological.

Novel(beastsOfPrey) → (Fantasy(beastsOfPrey) ∨ ScienceFiction(beastsOfPrey)) ∀x ∀y (ScienceFiction(x) ∧ Mythological(y) ∧ Creature(y) → ¬About(x, y)) About(beastsOfPrey, shetani) ∧ Creature(shetani) Mythological(shetani)

Beasts of prey is a fantasy novel.

Fantasy(beastsOfpPrey) ∧ Novel(beastsOfPrey)

True

Beasts of Prey is a fantasy novel or a science fiction novel, or both. Science fiction novels are not about mythological creatures Beasts of Prey Is about a creature known as the Shetani. Shetanis are mythological.

Novel(beastsOfPrey) → (Fantasy(beastsOfPrey) ∨ ScienceFiction(beastsOfPrey)) ∀x ∀y (ScienceFiction(x) ∧ Mythological(y) ∧ Creature(y) → ¬About(x, y)) About(beastsOfPrey, shetani) ∧ Creature(shetani) Mythological(shetani)

Beasts of prey isn't a science fiction novel.

¬ScienceFiction(beastsofprey) ∧ Novel(beastsOfPrey)

True

Beasts of Prey is a fantasy novel or a science fiction novel, or both. Science fiction novels are not about mythological creatures Beasts of Prey Is about a creature known as the Shetani. Shetanis are mythological.

Novel(beastsOfPrey) → (Fantasy(beastsOfPrey) ∨ ScienceFiction(beastsOfPrey)) ∀x ∀y (ScienceFiction(x) ∧ Mythological(y) ∧ Creature(y) → ¬About(x, y)) About(beastsOfPrey, shetani) ∧ Creature(shetani) Mythological(shetani)

A shetani is either mythological or a creature.

Mythological(shetani) ⊕ Creature(shetani)

False

Odell is an English surname originating in Odell, Bedfordshire. In some families, Odell is spelled O'Dell in a mistaken Irish adaptation. Notable people with surnames include Amy Odell, Jack Odell, and Mats Odell. Amy Odell is a British singer-songwriter. Jack Odell is an English toy inventor.

Surname(nameODell) ∧ From(nameODell, oDellBedfordshire) MistakenSpellingOf(nameO'Dell, nameODell) ∧ (∃x∃y(Family(x) ∧ Named(x, nameO'Dell) ∧ (¬(x=y)) ∧ Family(y) ∧ Named(y, nameO'Dell)) Named(amyODell, nameODell) ∧ NotablePerson(amyODell) ∧ Named(jackODell, nameODell) ∧ NotablePerson(jackODell) ∧ Named(matsODell, nameODell) ∧ NotablePerson(matsODell) British(amyODell) ∧ Singer(amyODell) ∧ SongWriter(amyODell) English(jackODell) ∧ ToyInventor(jackODell)

Jack Odell is a notable person.

NotablePerson(jackODell)

True

Odell is an English surname originating in Odell, Bedfordshire. In some families, Odell is spelled O'Dell in a mistaken Irish adaptation. Notable people with surnames include Amy Odell, Jack Odell, and Mats Odell. Amy Odell is a British singer-songwriter. Jack Odell is an English toy inventor.

Surname(nameODell) ∧ From(nameODell, oDellBedfordshire) MistakenSpellingOf(nameO'Dell, nameODell) ∧ (∃x∃y(Family(x) ∧ Named(x, nameO'Dell) ∧ (¬(x=y)) ∧ Family(y) ∧ Named(y, nameO'Dell)) Named(amyODell, nameODell) ∧ NotablePerson(amyODell) ∧ Named(jackODell, nameODell) ∧ NotablePerson(jackODell) ∧ Named(matsODell, nameODell) ∧ NotablePerson(matsODell) British(amyODell) ∧ Singer(amyODell) ∧ SongWriter(amyODell) English(jackODell) ∧ ToyInventor(jackODell)

Odell is Amy Odell's surname.

Named(amyODell, nameODell)

True

Odell is an English surname originating in Odell, Bedfordshire. In some families, Odell is spelled O'Dell in a mistaken Irish adaptation. Notable people with surnames include Amy Odell, Jack Odell, and Mats Odell. Amy Odell is a British singer-songwriter. Jack Odell is an English toy inventor.

Surname(nameODell) ∧ From(nameODell, oDellBedfordshire) MistakenSpellingOf(nameO'Dell, nameODell) ∧ (∃x∃y(Family(x) ∧ Named(x, nameO'Dell) ∧ (¬(x=y)) ∧ Family(y) ∧ Named(y, nameO'Dell)) Named(amyODell, nameODell) ∧ NotablePerson(amyODell) ∧ Named(jackODell, nameODell) ∧ NotablePerson(jackODell) ∧ Named(matsODell, nameODell) ∧ NotablePerson(matsODell) British(amyODell) ∧ Singer(amyODell) ∧ SongWriter(amyODell) English(jackODell) ∧ ToyInventor(jackODell)

Amy Odell is an English toy inventor.

English(amyODell) ∧ ToyInventor(amyODell)

Uncertain

Odell is an English surname originating in Odell, Bedfordshire. In some families, Odell is spelled O'Dell in a mistaken Irish adaptation. Notable people with surnames include Amy Odell, Jack Odell, and Mats Odell. Amy Odell is a British singer-songwriter. Jack Odell is an English toy inventor.

Surname(nameODell) ∧ From(nameODell, oDellBedfordshire) MistakenSpellingOf(nameO'Dell, nameODell) ∧ (∃x∃y(Family(x) ∧ Named(x, nameO'Dell) ∧ (¬(x=y)) ∧ Family(y) ∧ Named(y, nameO'Dell)) Named(amyODell, nameODell) ∧ NotablePerson(amyODell) ∧ Named(jackODell, nameODell) ∧ NotablePerson(jackODell) ∧ Named(matsODell, nameODell) ∧ NotablePerson(matsODell) British(amyODell) ∧ Singer(amyODell) ∧ SongWriter(amyODell) English(jackODell) ∧ ToyInventor(jackODell)

Amy Odell is also Amy O'Dell.

Named(amyODell, nameODell) ∧ Named(amyODell, nameO'Dell)

Uncertain

If you go somewhere by train, you will not lose time. If you go somewhere by car and meet a traffic jam, you will lose time. If you lose time, you will be late for work. Mary can get from New Haven to New York City either by train or car. Mary is late for work.

∀x (GoByTrain(x) → ¬LoseTime(x)) ∀x((GoByCar(x) ∧ Meet(x, trafficJam)) → LoseTime(x)) ∀x (LoseTime(x) → LateForWork(x)) FromAndTo(newHaven, newYork) ∧ (GoByTrain(mary) ⊕ GoByCar(mary)) LateForWork(mary)

Mary gets from New Haven to New York City by train.

FromAndTo(newHaven, newYork) ∧ GoByTrain(mary)

False

If you go somewhere by train, you will not lose time. If you go somewhere by car and meet a traffic jam, you will lose time. If you lose time, you will be late for work. Mary can get from New Haven to New York City either by train or car. Mary is late for work.

∀x (GoByTrain(x) → ¬LoseTime(x)) ∀x((GoByCar(x) ∧ Meet(x, trafficJam)) → LoseTime(x)) ∀x (LoseTime(x) → LateForWork(x)) FromAndTo(newHaven, newYork) ∧ (GoByTrain(mary) ⊕ GoByCar(mary)) LateForWork(mary)

Mary gets from New Haven to New York City by car.

FromAndTo(newHaven, newYork) ∧ GoByCar(mary)

True

If you go somewhere by train, you will not lose time. If you go somewhere by car and meet a traffic jam, you will lose time. If you lose time, you will be late for work. Mary can get from New Haven to New York City either by train or car. Mary is late for work.

∀x (GoByTrain(x) → ¬LoseTime(x)) ∀x((GoByCar(x) ∧ Meet(x, trafficJam)) → LoseTime(x)) ∀x (LoseTime(x) → LateForWork(x)) FromAndTo(newHaven, newYork) ∧ (GoByTrain(mary) ⊕ GoByCar(mary)) LateForWork(mary)

Mary meets a traffic jam.

Meet(mary, trafficJam)

Uncertain

If a person is hungry, the person is uncomfortable. If a person is uncomfortable, the person is unhappy.

∀x (Hungry(x) → Uncomfortable(x)) ∀x (Uncomfortable(x) → ¬Happy(x))

If a person is not hungry, the person is unhappy.

∀x (¬Hungry(x) → ¬Happy(x))

Uncertain

Tipped employees are not entitled to be paid the federal minimum wage by their employees. If a person is a white-collar worker, they are entitled to be paid the federal minimum wage by their employees. All lawyers are white-collar workers. Every advocate is a lawyer. Mary is not a lawyer or a tipped employee.

∀x (TippedEmployee(x) → ¬EntitledTo(x, federalMinimumWage)) ∀x (WhiteCollarWorker(x) → EntitledTo(x, federalMinimumWage)) ∀x (Lawyer(x) → WhiteCollarWorker(x)) ∀x (Advocate(x) → Lawyer(x)) ¬(Lawyer(mary) ⊕ TippedEmployee(mary))

Mary is a white-collar worker.

WhiteCollarWorker(mary)

Uncertain

Tipped employees are not entitled to be paid the federal minimum wage by their employees. If a person is a white-collar worker, they are entitled to be paid the federal minimum wage by their employees. All lawyers are white-collar workers. Every advocate is a lawyer. Mary is not a lawyer or a tipped employee.

∀x (TippedEmployee(x) → ¬EntitledTo(x, federalMinimumWage)) ∀x (WhiteCollarWorker(x) → EntitledTo(x, federalMinimumWage)) ∀x (Lawyer(x) → WhiteCollarWorker(x)) ∀x (Advocate(x) → Lawyer(x)) ¬(Lawyer(mary) ⊕ TippedEmployee(mary))

Mary is an advocate.

Advocate(mary)

False

Tipped employees are not entitled to be paid the federal minimum wage by their employees. If a person is a white-collar worker, they are entitled to be paid the federal minimum wage by their employees. All lawyers are white-collar workers. Every advocate is a lawyer. Mary is not a lawyer or a tipped employee.

∀x (TippedEmployee(x) → ¬EntitledTo(x, federalMinimumWage)) ∀x (WhiteCollarWorker(x) → EntitledTo(x, federalMinimumWage)) ∀x (Lawyer(x) → WhiteCollarWorker(x)) ∀x (Advocate(x) → Lawyer(x)) ¬(Lawyer(mary) ⊕ TippedEmployee(mary))

Mary is not an advocate.

¬Advocate(mary)

True

Tipped employees are not entitled to be paid the federal minimum wage by their employees. If a person is a white-collar worker, they are entitled to be paid the federal minimum wage by their employees. All lawyers are white-collar workers. Every advocate is a lawyer. Mary is not a lawyer or a tipped employee.

∀x (TippedEmployee(x) → ¬EntitledTo(x, federalMinimumWage)) ∀x (WhiteCollarWorker(x) → EntitledTo(x, federalMinimumWage)) ∀x (Lawyer(x) → WhiteCollarWorker(x)) ∀x (Advocate(x) → Lawyer(x)) ¬(Lawyer(mary) ⊕ TippedEmployee(mary))

Mary is either an advocate or a tipped employee.

Advocate(mary) ⊕ TippedEmployee(mary)

False

Tipped employees are not entitled to be paid the federal minimum wage by their employees. If a person is a white-collar worker, they are entitled to be paid the federal minimum wage by their employees. All lawyers are white-collar workers. Every advocate is a lawyer. Mary is not a lawyer or a tipped employee.

∀x (TippedEmployee(x) → ¬EntitledTo(x, federalMinimumWage)) ∀x (WhiteCollarWorker(x) → EntitledTo(x, federalMinimumWage)) ∀x (Lawyer(x) → WhiteCollarWorker(x)) ∀x (Advocate(x) → Lawyer(x)) ¬(Lawyer(mary) ⊕ TippedEmployee(mary))

If Mary is not both an advocate and is entitled to be paid the federal minimum wage by their employees, she is not a tipped employee.

(¬(Advocate(mary) ∧ EntitledTo(mary, federalMinimumWage))) → ¬TippedEmployee(mary)

True

Tipped employees are not entitled to be paid the federal minimum wage by their employees. If a person is a white-collar worker, they are entitled to be paid the federal minimum wage by their employees. All lawyers are white-collar workers. Every advocate is a lawyer. Mary is not a lawyer or a tipped employee.

∀x (TippedEmployee(x) → ¬EntitledTo(x, federalMinimumWage)) ∀x (WhiteCollarWorker(x) → EntitledTo(x, federalMinimumWage)) ∀x (Lawyer(x) → WhiteCollarWorker(x)) ∀x (Advocate(x) → Lawyer(x)) ¬(Lawyer(mary) ⊕ TippedEmployee(mary))

If Mary is either an advocate or a tipped employee, she is an advocate.

(Advocate(mary) ⊕ TippedEmployee(mary)) → Advocate(mary)

True

Asa Hoffmann was born in New York City. Asa Hoffman lives in Manhattan. Asa Hoffman is a chess player. Some chess players are grandmasters. People born and living in New York City are New Yorkers. People living in Manhattan live in New York City.

BornIn(asaHoffmann, newYorkCity) LiveIn(asaHoffmann, manhattan) ChessPlayer(asaHoffmann) ∃x ∃y (ChessPlayer(x) ∧ GrandMaster(x) ∧ (¬(x=y)) ∧ ChessPlayer(y) ∧ GrandMaster(y)) ∀x ((BornIn(x, newYorkCity) ∧ LiveIn(x, newYorkCity)) → NewYorker(x)) ∀x (LiveIn(x, manhattan) → LiveIn(x, newYorkCity))

Asa Hoffmann is a New Yorker.

NewYorker(asaHoffmann)

True

Asa Hoffmann was born in New York City. Asa Hoffman lives in Manhattan. Asa Hoffman is a chess player. Some chess players are grandmasters. People born and living in New York City are New Yorkers. People living in Manhattan live in New York City.

BornIn(asaHoffmann, newYorkCity) LiveIn(asaHoffmann, manhattan) ChessPlayer(asaHoffmann) ∃x ∃y (ChessPlayer(x) ∧ GrandMaster(x) ∧ (¬(x=y)) ∧ ChessPlayer(y) ∧ GrandMaster(y)) ∀x ((BornIn(x, newYorkCity) ∧ LiveIn(x, newYorkCity)) → NewYorker(x)) ∀x (LiveIn(x, manhattan) → LiveIn(x, newYorkCity))

Asa Hoffmann is a grandmaster.

GrandMaster(asaHoffmann)

Uncertain